The Fate of the Universe

Transcription

1 The Fate of the Universe How one set of equations changed an entire field of science Brian Kay PHY 495

2 Objective Examine the Friedmann equation and its impact on our understanding of the evolution of the universe Produce numerical and analytical solutions to the Friemann equation The results will provide us with the geometry, current age, and ultimate fate of the universe

3 Outline Part 1 - Early 20 th century cosmology Part 2 Understanding the Friedmann Equation Part 3 Solving the Friedmann equation

4 The Friedmann Equation

5 Part I The origins of cosmology

6 Alexander A. Friedmann ( ) The Man Who Made the Universe Expand ndr_fridman.png Soviet mathematician and meteorologist Most famous for contributions to cosmology First person to mathematically predict an expanding universe (1922) Derived from Einstein's general relativity Einstein initially dismissed Friedmann s equations as nothing more that a mathematical curiosity Developed his equation based on an isotropic and homogenous universe

7 Expanding Universe First general relativistic models by Einstein predicted a contracting universe (1917) Introduction of Cosmological Constant by Einstein 1922 the Friedmann equation predicted an expanding universe 1928 Georges Lemaitre independently concluded the same Lemaitre was the first to propose a primeval atom theory, later known as the Big Bang

8 Edwin Hubble Confirmed the existence of other galaxies besides the Milky way (1924) Vesto Slipher first discovered the Doppler shift in the spectra of galaxies, Hubble used this to prove the universe is expanding (1929) Velocities of receding galaxies from Earth are proportional to their distance from Earth Caused Einstein to abandon his cosmological constant

9 Hubble s Constant Gives the speed of a galaxy in km/s that is 1 Mpc away The inverse H 0-1 is known as Hubble time referred to as the expansion time scale Hubble first calculated H 0 to be 500 km s -1 Mpc -1 H 0 = 2.26 x s -1 H Gyr

10 Cosmic Microwave Background Radiation (CMB) Radiation from the Big Bang first theorized in 1948 by Gamow, Alpher, and Herman Steady State (SS) was an alternative theory develpoed in 1948 by Hoyle, Gold, and Bondi SS claimed that new matter was continuously being created as the universe expanded to keep the average density of matter equal over time Discovered in 1964 by radio astronomers Arno Penzias and Robert Wilson CMB caused most cosmologists to accept Big Bang and reject SS COBE ( ), WMAP ( ), Plank Spacecraft -No data yet Uniform distribution suggesting an isotropic and homogeneous universe The mean temperature is ± 0002 K

11 Rate of Expansion Two teams in the 1990 s set out to show the rate deceleration of the universe They both independently concluded the expansion is accelerating Appears to be a repulsive force countering gravity now dubbed dark energy Now cosmologists are reevaluating the importance of the cosmological constant

12 Part II Understanding the Friedmann Equation

13 Robertson-Walker Metric Derived from Einstein s general relativity A space-time metric that satisfies the principle of a homogeneous, isotropic universe The geometric structure should remain constant with time in comoving coordinates (r, θ, φ) and physical distances scale with a(t) Represents the κ value in the Friedmann equation with values of either (1, -1, 0)

14 Cosmic Scale Factor a(t) Represents relative expansion of the universe Dimensionless function of time Also called the Robertson-Walker scale factor Relates proper distance between a pair of objects undergoing isotropic and homogeneous expansion

15 Curvature Open, closed, flat Data suggests we live in a flat universe Derived from Robertson-Walker metric Κ is the curvature constant R 0 is the radius of curvature Determines how the universe will end

20 a(t) Matter Only ( κ = 1) Exact Solution These are closed universes with a finite time At some time in the future expansion will cease and all matter will collapse in on itself called the Big Crunch 12 Matter Only Positve Curvature H 0 t

25 Matter + Λ Curved Loitering is when during expansion a remains almost constant for a long period of time Could be a big bounce universe, however, we cannot calculate a present time with no beginning time Could lead to unphysical, forbidden range of the scale factor

26 a(t) Benchmark model Considered the best fit to the currently available observational data with t 0 = 14Gyr Is spatially flat and contains radiation, matter, and a dominant cosmological constant Benchmark Plot benchmark benchmark no radiation H 0 t

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